SIAM Journal on Applied Mathematics, Volume 80, Issue 1, Page 543-571, January 2020.
An age-structured model for the cell populations of the epidermis basal layer is proposed, with the aim of quantifying the cell production which makes possible epidermis renewal. The model, which extends our previous model [J. Math. Biol., 73 (2016), pp. 1595--1626], describes the dynamics of proliferating cells, differentiated cells, and apoptotic cells under the physical constraint on the total surface cell density imposed by the cell occupancy of a basement membrane. To fulfill this constraint during any dynamics, the surface cell density is assumed to control cell migration toward the epidermis suprabasal region, as well as the balance between production of proliferating and of differentiated cells at cell division. The well-posedness of the model is fully studied, and the unique steady state is characterized. Numerical simulations are provided for realistic values of the parameters, giving some insight into the stability of the equilibrium and into the homeostatic properties of the model.

中文翻译：

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表皮的基础层：在表面密度约束下细胞生产的数学模型

SIAM应用数学杂志，第80卷，第1期，第543-571页，2020年1月。
提出了年龄结构表皮基底层细胞群体的模型，目的是量化使表皮更新成为可能的细胞产量。该模型扩展了我们先前的模型[J. 数学。[Biol。，73（2016），pp。1595--1626]，描述了增殖细胞，分化细胞和凋亡细胞在基底膜细胞占据所施加的总表面细胞密度的物理约束下的动力学。为了在任何动力学过程中满足该约束，假定表面细胞密度控制着细胞向表皮上基底区的迁移，以及在细胞分裂时增殖细胞和分化细胞的产生之间的平衡。充分研究了模型的适定性，并表征了独特的稳态。